Meromorphic functions sharing a set with applications to difference equations

This paper is devoted to proving some uniqueness type results for an entire function f ( z ) that shares a common set with its shift f ( z + c ) or its difference operator Δ c f . We also give some applications to solutions of non-linear difference equations related to a conjecture proposed by C.C....

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 359; no. 1; pp. 384 - 393
Main Author Liu, Kai
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.11.2009
Elsevier
Subjects
Difference
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Finite order
Functions of a complex variable
Logarithmic difference
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Several complex variables and analytic spaces
Shared values
Shift
Uniqueness theory
Shift
Shared values
Uniqueness theory
Difference
Logarithmic difference
Finite order
Difference equation
Non linear equation
Linear equation
Mathematical analysis
Application
Entire function
Meromorphic function
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Summary:This paper is devoted to proving some uniqueness type results for an entire function f ( z ) that shares a common set with its shift f ( z + c ) or its difference operator Δ c f . We also give some applications to solutions of non-linear difference equations related to a conjecture proposed by C.C. Yang.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.05.061